"It gets a bit stretched," says Dr Joanne Topping. As a description of the growing pressures the consultant obstetrician and her colleagues in the maternity unit at Liverpool women's hospital are under, that turns out to be a notable understatement. A 25% leap in the number of babies born over the past decade, the highest birthrate in 40 years, the increasing challenge posed by medical problems in pregnant women such as obesity, and ongoing understaffing mean that NHS maternity units are struggling to deliver the ideal birth experience that all mothers-to-be are seeking at such a joyous, though also often stressful, time.

LWH, or "the Women's" as locals call it, delivers more babies than anywhere else in Europe; about 8,500 a year, which is almost one an hour, every day of the year. One of only two hospitals in England that specialise in looking after women and their babies, it has a great reputation on Merseyside and is popular and respected after delivering generations of Liverpudlians' offspring. Scores of thank-you cards adorn its lilac and blue-grey walls. "Thank you so much for delivering our beautiful baby girl. Sorry for shouting at you," reads one.

But, like every other maternity unit, it is increasingly hard-pushed to cope with the rising numbers of women needing care before, during and after giving birth. It gave the Guardian access during a typical Monday to see how it is doing. Tellingly, in the past 15 months the sheer demand for its services has forced it to temporarily close its doors on three occasions, for six to 12 hours at a time, for the first time in its history.

Thank-you cards pinned to a board at the hospital, where 8,500 babies are born a year. Photograph: Christopher Thomond Christopher Thomond/Christopher Thomond

This forced women who were ready to give birth there to go elsewhere. "On some days, we just didn't have anywhere to put people – some of that was due to the complexity of the cases we already had and some of it was due to staffing," recalls Topping. "We had enough capacity for the women that were in, but if we had admitted more women at that stage we wouldn't have been able to care for them. It's the first time it's happened in this unit, but it's not unusual for us to receive phonecalls from nearby places such as Warrington, Whiston and Ormskirk saying they're closed due to capacity issues. They advise their women to come to us instead," she adds.

As with almost every NHS maternity unit, LWH does not always have enough staff on duty. Inevitably, there are consequences. When Care Quality Commission inspectors made an unannounced visit in July, the feedback from most mothers and their relatives was "very positive", they found. "People described the care and treatment they had received as 'excellent' [and] 'brilliant' and they described staff as 'amazing' and 'approachable'. People felt safe and confident in the ability and experience of the staff supporting them," their report said. Mothers had both good experiences and good outcomes, the CQC added.

But "people did also tell us they felt the staff were 'too busy' and 'very busy' and felt this prevented them from asking for too much support." This is typical of more and more of the CQC's reports on hospitals generally. Patients say most staff are very good most of the time, but see them often being close to run off their feet and do not blame them for care sometimes being less than ideal.

Understaffing, which is closely linked to the NHS's £20bn efficiency drive, is a problem across the service. At LWH, inspectors found there were too few doctors, midwives and healthcare assistants. Some women had to wait hours for pain relief, or did not have their call bell answered immediately or did not bother visibly busy staff to help them breastfeed. David Cameron's pledges to give the NHS 5,000 more midwives and protect the service's fabled frontline ring hollow at LWH.

"The doctor looking after me keeps getting taken away because there's an emergency or someone else needs her more," one woman told the CQC. Interestingly, staff shared the patients' concerns. "Emotional care and support" for women suffered, they said. "Staff reported a couple of shifts recently when one corridor of single rooms accommodating up to 17 women and babies had been staffed by only one healthcare assistant," the CQC said. Sometimes, mothers spending their first few hours with their newborn have to be moved elsewhere because the sheer number of births means their room is needed for a woman in labour. "They end up being looked after by a different midwife, which disrupts their continuity of care. That's not ideal for anyone and can lead to a poor patient experience, but is probably unavoidable," says Topping, who is also the hospital's overall clinical director for maternity care.

LWH has to save £4m this year, despite the baby boom increasing its workload. "A unit this size should have a consultant present 24/7. At the moment we usually have that for 14 or 15 hours a day. Our aim is 24/7, but that would need us to have four more consultants, which would cost £400,000. Given our £4m cost-saving target, realistically we aren't going to get those consultants," says Topping. The recruitment of 20 extra midwives since the CQC visit has helped, though.

During the Guardian's visit, staff delivered 26 babies during a typically busy day. In the privacy of their own room, Rachael and Andy Birley are a picture of contentment as they cuddle their new daughter, Lauren, who arrived at 10.47, weighing 3.7kg. She coos happily, like a purring cat. They have had a positive and euphoric experience, especially compared with the arrival 22 months ago of William, their first child. "My labour with Lauren was eight and a half hours, whereas it was three and a half days with William, and then I was in for three days after that as he wouldn't feed initially," explains Rachael.

"With William, it got complicated and multiple people just poured into the room, consultants and midwives, about 12 of them. A decision was taken to get him out and he ended up being a forceps delivery. But today it was just one midwife and a student doctor, which made it a lot less stressful," says Rachael. Both are full of praise for their midwife, Paula Cato. "She was with me all the way through and was great. She was calm and she kept me calm. I wasn't left alone for any length of time," adds the 34-year-old.

Her only disappointments were having to stop using an exercise ball because it was slowing down her contractions, and not getting the water birth she wanted in one of the unit's two pools. "I was told that would be dangerous because I had had diamorphine for pain relief and that could have made me sleepy in the water." Andy, a 36-year-old financial adviser, says: "I buzzed a few times because Rachael was getting distressed and they came straight in." The couple say are very happy with their care.

Childbirth is routine – about 800,000 women a year give birth in the UK – but is also unpredictable. While many births occur in hospital, at home or in a doctor-free midwife-led unit (MLU) for low-risk pregnancies – 2,500 of LWH's 8,500 annual births come in its MLU – more and more arrivals are proving complicated and potentially risky. Most women want a straightforward, natural birth. But almost one in three end up having their baby with the help of some form of medical intervention. Of the 26 babies born that day at LWH, 17 were girls and nine were boys. Three arrived overnight, the first at 01.15, and the last at 23.38. But just 13 of the 26 mothers had a normal vaginal birth. Of the other 13, three needed an emergency caesarean section and five had a planned C-section, while four babies were delivered using forceps and one using ventouse, a sort of suction cup.

Three involved serious complications. One woman suffered from placenta praevia, in which the placenta came down before the baby, completely covering the cervix. That can trigger what is known as "torrential haemorrhage", severe bleeding, in the woman during labour, which can put her life in danger. In this case, the woman had a spinal anaesthetic, then a planned C-section at 10.59 to get her baby out safely. Her condition, detected in pregnancy, made that unavoidable. She did suffer a haemorrhage, losing 1.25l of blood in the process; about two and a half pints, much more than the 300-500mls a woman usually loses while giving birth. Luckily for her, LWH is one of the few places with a cell-saver machine available 24/7, which collected and "washed" her lost blood so it could be given back to her, meaning she did not need any from a donor.

Mid-afternoon, another woman had an emergency C-section for "deep transverse arrest": she had reached the second stage of labour but her child came down the birth canal in the wrong position, with its head rotated about 45 degrees, making a normal delivery very difficult. The mother lost 800mls of blood. And at 20.45, staff performed a rotational forceps delivery to rotate a baby's head into the right position to allow it to be helped down the birth canal and born vaginally – the entire labour took 16 hours.

Candace Knight with her son Amadi, who was born after 25 weeks and three days of pregnancy. Photograph: Christopher Thomond Christopher Thomond/Christopher Thomond

Cathy Atherton, the LWH's head of midwifery, cites many reasons beyond the baby boom and understaffing for the growing pressures they are under. They include the growing numbers of mothers who are obese, or have another underlying medical condition, or mental health problems, or are older – being over 35, especially over 40, involves extra risk – or who do not speak English. All these require more resources and more of the staff's time.

These days, LWH provides services that did not exist a few years ago, such as antenatal clinics with translators and female-only doctors for the growing number of women from China, eastern Europe and African countries such as Somalia, as well as a dedicated perinatal mental health service, where psychiatrists and community psychiatric nurses, as well as midwives and obstetricians, provide help, advice and treatment. There is also a pre-term labour clinic for women who have previously gone into labour prematurely and tests for those with severe hypertension in pregnancy, as they could develop into pre-eclampsia, which can lead to the woman suffering a fit and losing her baby, explains Atherton.

In LWH's neonatal unit, Candace Knight is adjusting to life with a very premature baby. Her son, Amadi, was born after just 25 weeks and three days of pregnancy, though tests have not identified why. He weighed just 845g, though has since grown to 995g. His first kilo is in sight. His birth illustrates a quiet scandal of maternity care: the national shortage of cots – incubators – for those born worryingly early.

Knight, a 23-year-old deputy manager for the bookmakers William Hill, lives in Birmingham. But when it became obvious at 24 weeks and three days that her baby's birth was imminent, Birmingham women's hospital did not have a cot available. LWH did, though, prompting a four-hour trip for Knight in an ambulance up the M6 in terrible traffic.

Home for Amadi now is an incubator at LWH, not a moses basket or his mother's arms. After an initial burst of breathing for himself, he is now on a ventilator. Knight has just moved into a flat provided by LWH and spends about 14 hours a day beside her son, as well as visiting him about 4am or 5am every day, touching him occasionally through doors that look like portholes.

Infection control at this stage is vital. "I still express milk every couple of hours, change his nappy, wipe his face and put talcum powder under his arms. "I can hold him, but only when he's well enough and there's a nurse around. He's getting tiny bits of my milk, he's on a fluid drip for nutrition and they say it'll be weeks rather than days before he's off the ventilator. Even now there's still a 40% chance he could die," explains Knight matter of factly. She is delighted with the care Amadi is receiving.

Women's greater expectations of how their birth should be have added to the pressures, as have the choice of place of birth that successive governments have promised mothers, such as the right to have a baby at home, in an MLU or in a consultant-led obstetric unit. The pressure on resources makes such choices impossible to realise for some women. Expectant mothers are also more savvy, and know they can have a range of types of pain relief if they ask.

On top of this, rising maternal obesity "is a major factor", says Topping. "If you have 20cm of fat on you rather than 5cm, that can make it harder to give you your 12- and 20-week scans and means you are at greater risk of developing gestational diabetes and also of having a stillbirth or C-section or being induced."

The number of women like that has "almost doubled" in Topping's 15 years as a consultant, she reckons. "These women need more tests, more clinicians' time, more monitoring, more medication and more intervention. Obesity is one of the things that make the job more challenging these days." But, as a recent National Audit Office report showed, the money going into maternity care – now £2.6bn a year in England – has not kept up with rising demand and growing complexity.

The trend towards older motherhood is less of a burden than reports have suggested, the obstetrician thinks. But women giving birth for the first time over the age of 35, and especially once they are 40 or above, or giving birth again after a long gap, perhaps because they have remarried, represent "a big societal shift and new dynamic that's not previously been there". Such women may be at greater risk of having a baby with a chromosomal disorder, such as Down's syndrome, or needing or wanting a C-section. People's desire to exercise choice means the government's target of reducing C-sections from 25% to 20% of all births is unattainable, Topping believes.

"Midwifery is as caring and compassionate as ever. But it's more difficult than it used to be. The birthrate means the demands are now very, very high, we get short-staffed and it's getting harder to give every woman the time they want or need when we are so busy," says Sarah McGrath, a midwife for 24 years. The round-the-clock nature of childbirth means the reception desk for the maternal assessment unit, where women who are anxious about their pregnancy can come, is now staffed 24 hours a day. LWH's telephone triage service, which pregnant women who are anxious because they have experienced some bleeding or have not felt their baby move for a few hours can ring, went 24/7 in March too.

So now, while women's need for help from the NHS with their birth and afterwards with their baby is only growing, the number of doctors, midwives, nurses and other NHS staff whose job is to make every woman's birth the special experience she hopes for – "her World Cup", as one midwife put it – are fewer than needed to achieve that ambition.

• This article was amended on 6 December 2013. An earlier version said that LWH was obliged to close on four occasions in the past 15 months. That should have been three occasions.